Error in A115866

[Max Alekseyev]

There is another recurrence with coefficients of degree 2:

- (2*n^2 + 4*n + 2) * a(n) + (5*n^2 + 13*n + 8) * a(n+1) - (111*n^2 +
438*n + 417) * a(n+2) - (55*n^2 + 389*n + 685) * a(n+3) + (n^2 + 8*n +
16) * a(n+4) = 0

or in the factored form:

- 2*(n+1)^2 * a(n) + (n+1)*(5n+8) * a(n+1) - 3*(37*n^2 + 146*n + 139)
* a(n+2) - (55*n^2 + 389*n + 685) * a(n+3) + (n+4)^2 * a(n+4) = 0.

Max

On 3/3/07, Alec Mihailovs <alec at mihailovs.com> wrote:
> ----- Original Message -----
> From: "David W. Cantrell" <DWCantrell at sigmaxi.net>
>
>
> > On Saturday, March 03, 2007, "Nick Hobson" <nickh at qbyte.org> wrote:
> >
> >> Is there  a recurrence equation for this sequence, analogous to
> >> a(-1) = a(0) = 1;  n*a(n) = 3*(2*n-1)*a(n-1) - (n-1)*a(n-2), for
> >> A001850 (the 2-dimensional  equivalent sequence)?
> >
> > Good question. I don't know. The recurrence I had used is the same as
> > yours at the end below.
>
> GFUN gives the following recurrence:
>
> gfun:-listtorec(L,a(n));
>
>                     2      3
>   [{(8 + 19 n + 14 n  + 3 n ) a(n)
>
>                              2      3
>          + (-54 - 92 n - 51 n  - 9 n ) a(n + 1)
>
>                                   2        3
>          + (1771 + 2488 n + 1140 n  + 171 n ) a(n + 2)
>
>                  2                  3
>          + (-23 n  - 57 n - 45 - 3 n ) a(n + 3), a(0) = 1, a(2) = 409,
>
>         a(1) = 13}, ogf]
>
> Alec Mihailovs
> http://mihailovs.com/Alec/
>
>
>